I suggest starting by cleaning the paint with a gentle automotive finish cleaner, then following with a clay bar with appropriate lubricant. A clay bar is more gentle than polishing compound and will remove grime and dead paint. If the clay bar doesn't achieve the effect you're after, then follow up with a polishing compound. Be advised that polishing compound can wear your paint down to primer if you're too aggressive with it; especially if the paint is old and thin. If the clay bar works, follow it up with any good wax. I like to put down a sealing coat of poly such as Rejex, then a cover coat of a good carnauba. I've gotten excellent results with Mother's California Gold, but there are numerous excellent carnauba's out there.